How do you find the domain of inverse trig functions?

1 Answer
George C.
May 24, 2015

The domain of any inverse trig function (#arcsin#, #arccos#, #arctan#) is equal to the range of the corresponding trig function (#sin#, #cos#, #tan#).

So the domain of #arcsin# and #arccos# is #{x in RR : -1 <= x <= 1}# since #-1 <= sin theta <= 1# and #-1 <= cos theta <= 1# for all #theta in RR#.

The domain of #arctan# is #RR# since the range of #tan theta# is the whole of #RR#.

The domain of #sec^-1# and #csc^-1# is #{x in RR : x <= -1 or x >= 1}#

The domain of #cot^-1# is #RR#.

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